The actress will join Julie Andrews and Matthew Goode in the film, which is due to start shooting in the UK this summer.
Crooked House centres on the unsolved mystery of a patriarch's murder, the house of the title referring to the mansion shared by three generations of his family who all have a grudge to bear.
The detective will be the fiancé of the murdered millionaire's granddaughter, who is unable to marry him until he finds the killer.
Gosford Park writer Julian Fellowes has adapted the novel for the screen.
Arterton has also committed to Neil Jordan's Byzantium, in which she will play one half of a mother and daughter vampire duo with Hanna's Saoirse Ronan.